Thermodynamics of Fatigue: Degradation-Entropy Generation Methodology for System and Process Characterization and Failure Analysis

Formulated is a new instantaneous fatigue model and predictor based on ab initio irreversible thermodynamics. The method combines the first and second laws of thermodynamics with the Helmholtz free energy, then applies the result to the degradation-entropy generation theorem to relate a desired fatigue measure—stress, strain, cycles or time to failure—to the loads, materials and environmental conditions (including temperature and heat) via the irreversible entropies generated by the dissipative processes that degrade the fatigued material. The formulations are then verified with fatigue data from the literature, for a steel shaft under bending and torsion. A near 100% agreement between the fatigue model and measurements is achieved. The model also introduces new material and design parameters to characterize fatigue.

Integrated Semigroups on Fréchet Spaces II: F_sBSV ([a,b],F)-space, FsLip_0,w([0,+∞),F)-space, Isometric Theorem and Application

In this article we will study the Riemann Stieltjes Laplace integral of vectorial functions in Fréchet spaces. Particularly we will prove a isometric theorem and a generation theorem for integrated semigroups on Fréchet spaces.

A Thermodynamic Model for Lithium-Ion Battery Degradation: Application of the Degradation-Entropy Generation Theorem

Presented is a lithium-ion battery degradation model, based on irreversible thermodynamics, which was experimentally verified, using commonly measured operational parameters. The methodology, applicable to all lithium-ion batteries of all chemistries and composition, combined fundamental thermodynamic principles, with the Degradation–Entropy Generation theorem, to relate instantaneous capacity fade (loss of useful charge-holding capacity) in the lithium-ion battery, to the irreversible entropy generated via the underlying dissipative physical processes responsible for battery degradation. Equations relating capacity fade—aging—to battery cycling were also formulated and verified. To show the robustness of the approach, nonlinear data from abusive and inconsistent battery cycling was measured and used to verify formulations. A near 100% agreement between the thermodynamic battery model and measurements was achieved. The model also gave rise to new material and design parameters to characterize all lithium-ion batteries.

Rule-Generation Theorem and its Applications

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical theories via rules of special sort was developed successfully by Negri and von Plato. In this paper a general theorem on possible ways of transforming axiomatic sequents into rules in sequent calculi is proved. We discuss its possible applications and provide some case studies for illustration.

Proposal of Micro Removal Process with Pulsed Laser Irradiation Based on Form Generation Theorem

In general, the form generation theorem of laser removal processes has not yet been established. The cause of this is that laser is a light source and has no tool shape as conventional machining tools. Therefore, its transcription characteristics could not be determined. In this paper, the application of the form generation theorem to laser removal process is examined experimentally. In order to establish the form generation theorem, first the “equivalent tool shape” of the focused beam is determined. To determine the equivalent tool shape, a groove is machined with the laser intensity just above the removal threshold of the work piece material. From the machining result, the cross-section of the groove is machined in to a V-shape. The V-shape is peculiar to the workpiece material, thus can be determined as equivalent tool shape of laser machining. The groove shape can be simulated numerically by considering the removal threshold and dependence of absorption characteristics to incidence angle. The numerical simulation and the experimental result were in good agreement. Based on the equivalent tool shape and the form generation theorem, a rectangular cross-section groove is experimented. As a result the groove was finished with a flat bottom having ruggedness like a saw-blade. This result indicates that the laser shaping based on the form generation theorem can be possible by laser irradiation with properly suppressed intensity.

A GENERATION THEOREM FOR GROUPS OF FINITE MORLEY RANK

We deal with two forms of the "uniqueness cases" in the classification of large simple K*-groups of finite Morley rank of odd type, where large means the 2-rank m2(G) is at least three. This substantially extends results known for even larger groups having Prüfer 2-rank at least three, so as to cover the two groups PSp 4 and G 2. With an eye towards more distant developments, we carry out this analysis for L*-groups, a context which is substantially broader than the K* setting.

Application of Degradation-Entropy Generation Theorem to Dry Sliding Friction and Wear

The Entropy Generation Theorem recently formulated by Bryant, Khonsari and Ling [1] relates any form of degradation to the irreversible dissipative processes germane to the degradation mechanism. The theorem was formulated and proved [1] based on the first and second laws of thermodynamics In this article, dry sliding wear will be related to dry sliding friction through application of the theorem. The result reproduces the Holm-Archard wear law, but with a wear coefficient based on measurement of temperatures and wear volume lost.